• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.945-956
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• 2020

We introduce the concept of S-exchange rings to unify various subclass of exchange rings, where S is a subset of the ring. Many properties on S-exchange rings are obtained. For instance, we show that a ring R is clean if and only if R is left U(R)-exchange, a ring R is nil clean if and only if R is left (N(R) - 1)-exchange, and that a ring R is J-clean if and only if R is left (J(R) - 1)-exchange. As a conclusion, we obtain a sufficient condition such that clean (nil clean property, respectively) can pass to corners and reprove that J-clean passes to corners by a different way.

• Journal of The Korean Astronomical Society
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• v.34 no.1
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• pp.47-57
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• 2001

In this paper we have reconstructed an armillary sphere based on the Method of an Armillary Sphere Making described in the Volume 1 of The Collection of Writings on the Scientific Instruments-Uigijipsol (儀器輯說, two volumes) edited in the 1850's by Nam Byong-Chul (南秉哲, 1817-1863) who was a famous Korean states-man-scientist. Nam achieved convenience and accuracy in the measurements of stellar positions in the manner of selective setting the equatorial, ecliptic and horizontal poles by adding a pole axis exchange ring called Jaigeukkwon (載極圈) between the Three Arrangers of Time and Four Displacements. We made use of 3-dimensional graphic software for modelling Nam's armillary sphere which consisted of five layers-eight rings. Results of simulation showed that the pole axis exchange ring functioned properly in setting the equatorial, ecliptic and horizontal coordinates simply by exchange of positions of specified holes on the ring. We ascertained that the invention of Jaigeukkwon solved inherent problems in the conventional Chinese armillary sphere in computation of real ecliptic coordinates. It was revealed that Nam Byong-Chul made great contributions in the East Asian history of armillary sphere making.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.59-66
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• 2008

Keskin and Harmanci defined the family B(M,X) = ${A{\leq}M|{\exists}Y{\leq}X,{\exists}f{\in}Hom_R(M,X/Y),\;Ker\;f/A{\ll}M/A}$. And Orhan and Keskin generalized projective modules via the class B(M, X). In this note we introduce X-local summands and X-hollow modules via the class B(M, X). Let R be a right perfect ring and let M be an X-lifting module. We prove that if every co-closed submodule of any projective module P contains Rad(P), then M has an indecomposable decomposition. This result is a generalization of Kuratomi and Chang's result [9, Theorem 3.4]. Let X be an R-module. We also prove that for an X-hollow module H such that every non-zero direct summand K of H with $K{\in}B$(H, X), if $H{\oplus}H$ has the internal exchange property, then H has a local endomorphism ring.

• Bulletin of the Korean Chemical Society
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• v.16 no.3
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• pp.248-251
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• 1995

The crystal structure of Ba46-X, Ba46Al92Si100O384 [a= 25.297(1) Å], has been determined by single-crystal X-ray diffraction techniques in the cubic space group Fd&bar{3}at 21(1) ℃. The crystal was prepared by ion exchange in flowing stream of 0.05 M Ba(OH)2 aqueous solution for 5 days. The crystal was then dehydrated at 380 ℃ and 2 × 10-6 Torr for 2 days. The structure was refined to the final error indices R1= 0.051 and Rw= 0.054 with 369 reflections for which I > 3σ(I). In this structure, all Ba2+ ions are located at the three different crystallographic sites: fourteen Ba2+ ions are located at site Ⅰ, the centers of the double six rings, two Ba2+ ions lie at site Ⅰ', in the sodalite cavity opposite double six rings(D6R's) and another thirty Ba2+ ions are located at site Ⅱ in the supercage. Two Ba2+ ions are recessed ca. 0.27 Å into the sodalite cavity from their three O(3) oxygen plane and thirty Ba2+ ions are recessed ca. 1.11 Å into the supercage from their three O(2) oxygen planes, respectively (Ba(1)-O(3) = 2.76(1) Å, O(3)-Ba(1)-O(3) = 180(0)°, Ba(2)-O(3) = 2.45(1) Å, O(3)-Ba(2)-O(3) = 108(1)°, Ba(3)-O(2)=2.65(1) Å, and O(2)-Ba(3)-O(2)=103.9(4)°).

• Bulletin of the Korean Chemical Society
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• v.16 no.9
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• pp.823-826
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• 1995

The crystal structure of a sulfur sorption complex of the dehydrated partially Co2+ exchanged zeolite A (a=12.058(2) Å) has been determined by single-crystal X-ray techniques. The crystal structure was solved and refined in cubic space group Pm3m at 21(1) ℃. Ion Exchange with aqueous 0.05 M Co(NO3)2 was done by the static method. The crystal of Na4Co4-A was dehydrated at 380 ℃ and 2 × 10-6 Torr for 2 days, followed by exposure to about 100 Torr of sulfur at 330 ℃ for 72 h. Full matrix least-squares refinement converged to R1=0.084 and Rw=0.074 with 102 reflections for which I > 3σ(I). Crystallographic analysis shows that 2.8 Co2+ ions and 4 Na+ ions per unit cell occupy 6-ring sites on the threefold axes. 1.2 Co2+ ions occupy the 8-ring sites on fourfold axes. 2.8 Co2+ ions at Co(1) are recessed 0.66 Å into the large cavity and 4 Na+ ion at Na(1) are recessed 0.77 Å into the sodalite cavity from the (111) plane of O(3)'s. Approximately 16 sulfur atoms were sorbed per unit cell. Two S8 rings, each in a butterfly form, are found in the large cavity. The bond length between S and its adjacent S is 2.27(3) Å. The distance between 6-ring Co2+ ion and its adjacent sulfur is 2.53 (2) Å and that between 8-ring Co2+ ions and its adjacent sulfur is 2.72(9) Å. The angles of S-S'-S and S'-S-S'/ in octasulfur rings are 119.0(2)°and 113.0(2)°, respectively.

• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1193-1205
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• 2018

We focus our attention on a ring property that nilpotents are contained in the Jacobson radical. This property is satisfied by NI and left (right) quasi-duo rings. A ring is said to be NJ if it satisfies such property. We prove the following: (i) $K{\ddot{o}}the^{\prime}s$ conjecture holds if and only if the polynomial ring over an NI ring is NJ; (ii) If R is an NJ ring, then R is exchange if and only if it is clean; and (iii) A ring R is NJ if and only if so is every (one-sided) corner ring of R.

• Magazine of the Korean Society of Agricultural Engineers
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• v.17 no.2
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• pp.3763-3771
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• 1975

This study was attempted to investigate the changes of specific fuel consumption, compression pressure and power output, consequently to obtain basic data on farm kerosene engine. The samples which are used in this study are a 4 cycle water cooled korosene engine for the use of K6-CT83 power tiller and a 4 cycle air-cooled kerosene engine for the use of G5L-3A water pump. The Korean Industrial Standards (K.S)KS-B 6002 "Test code of small internal combustion engine" was referred in carrying out this study, and its results are as follows. 1. According to load increasing, the speific fuel consumption of the engines generally decreases, however, in case of 10% over-loading it increases. 2. As a result of full load consecutive operation, according to passing of operating time, the amount of wear generally increases, consequently the speific fuel consumption also increases, and inversly the compression pressure decreases. 3. The changes of specific fuel consumption and compression pressure were closely related with time of piston ring exchange, and periodically about 100 hours the engines show the increase of specific fuel consumption and the decrease of compression pressure. 4. After about 300 hours, although the engine had new piston rings, the specific fuel consumption increase, consequently the engine needs boring. In actual use, it is impossible to operate consecutively on full load, therefore the boring time of engine is expected to come later.

• Bulletin of the Korean Chemical Society
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• v.29 no.9
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• pp.1711-1716
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• 2008

The reaction of copper(II) chloride with phenyl-N-[(pyridine-2-yl)methylene]methaneamide (ppmma) leads to a new $\mu$ -chloro bridged dimeric [Cu(ppmma)$Cl_2$]$_2$ complex, whereas a reaction of copper(II) bromide with ppmma affords a monomeric Cu(ppmma)$Br_2$ complex. Both complexes have been characterized by X-ray crystallography and electronic absorption spectroscopy. The crystal structural analysis of [Cu(ppmma)$Cl_2$]$_2$ shows that the two Cu(II) atoms are bridged by two chloride ligands, forming a dimeric copper(II) complex and the copper ion has a distorted square-pyramidal geometry ($\tau$ = 0.2). The dimer units are held through a strong intermolecular $\pi-\pi$ interactions between the nearest benzyl rings. On the other hand, Cu(ppmma)Br2 displayed a distorted square planar geometry with two types of strong intermolecular π-π interaction. EPR spectrum of [Cu(ppmma)$Cl_2$]$_2$ in frozen glas s at 77 K revealed an equilibrium between the mononuclear and binuclear species. The magnetic susceptibilities data of [Cu(ppmma)$Cl_2$]$_2$ and Cu(ppmma)$Br_2$ follow the Curie-Weiss law. No significant intermolecular magnetic interactions were examined in both complexes, and magnetic exchange interactions are discussed on the basis of the structural features.

• Journal of the Korean Chemical Society
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• v.43 no.4
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• pp.384-385
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• 1999

Two anhydrous crystal structures of fully dehydrated, $Ca^{2+}$- and $Tl^+$-exchanged zeolite X, TEX>$Ca_{18}Tl_{56}Si_{100}Al_{92}O_{384}($Ca_{18}Tl_{56}$-X;\alpha=24.883(4)\AA)$ and TEX>$Ca_{32}Tl_{28}Si_{100}Al_{92}O_{384}($Ca_{32}Tl_{28}$-X;\alpha=24.973(4)\AA)$ per unit cell, have been determined by single-crystal X-ray diffraction techniques in the cubic space group Fd3 at $21(1)^{\circ}C.$ $Ca_{18}Tl_{56}-X$ was prepared by ion exchange in a flowing stream of 0.045 M aqueous $Ca(NO_3)_2$ and 0.005 M $TlNO_3$. $Ca_{32}Tl_{28}-X$ was prepared similarly using a mixed solution of 0.0495 M $Ca(NO_3)_2$ and 0.0005M $TlNO_3$. Each crystal was then dehydrated at 360 $^{\circ}C$ and $2{\times}10^{-6}$ Torr for 2 days. Their structures were refined to the final error indices, $R_1=0.039\;and\;R_2=0.036$ with 382 reflections for $Ca_{18}Tl_{56}-X$ , and $R_1=0.046\;and\;R_2=0.045$ with 472 reflections for $Ca_{32}Tl_{28}$-X for which $/>3\sigma(I).$ In the structures of dehydrated $Ca_{18}Tl_{56^-}X\;and\;Ca_{32}Tl_{28}$-X, $Ca^{2+}\;and\;Tl^+$ ions are located at six crystallographic sites. Sixteen $Ca^{2+}$ ions fill the octahedral sites I at the centers of double six rings ($Ca_{18}Tl_{56}$-X:Ca-O=2.42(1) and O-Ca-O=93.06(4)$^{\circ}$; $Ca_{32}Tl_{28}$-X Ca-O=2.40(1) $\AA$ and O-Ca-O=93.08(3)$^{\circ}$). In the structure of $Ca_{18}Tl_{56}$-X, another two $Ca^{2+}$ ions occupy site II (Ca-O=2.35(2) $\AA$ and O-Ca-O=111.69(2)$^{\circ}$) and twenty six $Tl^+$ ions occupy site II opposite single six-rings in the supercage; each is 1.493 $\AA$ from the plane of three oxygens $(Tl-O=2.70(8)\AA$ and O-Tl-O=92.33(4)$^{\circ}$). About four $Tl^+$ ions are found at site II',1.695 $\AA$ into sodalite cavity from their three oxygen plane (Tl-O=2.81 (1) and O-Tl-O=87.48(3)). The remaining twenty six $Tl^+$ ions are distributed over site III'(Tl-O=2.82 (1) $\AA$ and Tl-O=2.88(3)$^{\circ}$). In the structure of $Ca_{32}Tl_{28}$-X, sixteen $Ca^{2+}$ ions and fifteen $Tl^+$ ions occupy site III' (Ca-O=2.26(1) $\AA$ and O-Ca-O=119.14(4)$^{\circ}$; Tl-O=2.70(1) $\AA$ and O-Tl-O=92.38$^{\circ}$) and one $Tl^+$ ion occupies site II'. The remaining twelve $Tl^+$ ions are distributed over site III'. It appears that $Ca^{2+}$ ions prefer sites I and II in that order and $Tl^+$ ions occupy the remaining sites.